(5-2i)(3-6i)=0

Solution for (5-2i)(3-6i)=0 equation:

Simplifying
(5 + -2i)(3 + -6i) = 0

Multiply (5 + -2i) * (3 + -6i)
(5(3 + -6i) + -2i * (3 + -6i)) = 0
((3 * 5 + -6i * 5) + -2i * (3 + -6i)) = 0
((15 + -30i) + -2i * (3 + -6i)) = 0
(15 + -30i + (3 * -2i + -6i * -2i)) = 0
(15 + -30i + (-6i + 12i2)) = 0

Combine like terms: -30i + -6i = -36i
(15 + -36i + 12i2) = 0

Solving
15 + -36i + 12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -12i + 4i2) = 0

Factor a trinomial.
3((1 + -2i)(5 + -2i)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

Solving
1 + -2i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Subproblem 2
Set the factor '(5 + -2i)' equal to zero and attempt to solve:

Simplifying
5 + -2i = 0

Solving
5 + -2i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2i = 0 + -5
-2i = 0 + -5

Combine like terms: 0 + -5 = -5
-2i = -5

Divide each side by '-2'.
i = 2.5

Simplifying
i = 2.5
Solution
i = {0.5, 2.5}